A wide range of porous materials, from lyotropic liquid crystals [1] to brain tissue [2], contain anisotropic pores with varying sizes, shapes, and degrees of alignment on mesoscopic length scales. A complete characterization of the material requires estimation of all these parameters, but unfortunately their effects on the detected MRI (Magnetic Resonance Imaging) signal are hopelessly entangled when using conventional diffusion MRI methods based on the Stejskal-Tanner sequence [3] with two magnetic field gradient pulses. This sequence may in the following be referred to as the single pulsed field gradient (sPFG) sequence or experiment.
In diffusion MRI (dMRI), each voxel (which typically may be of a millimeter-size) of the image contains information on the micrometer-scale translational displacements of the water [15]. sPFG is used in diffusion tensor imaging (DTI), enabling quantification of mean diffusion (MD, also apparent diffusion coefficient, ADC) and diffusion anisotropy (Fractional Anisotropy, FA). Although sPFG-based DTI measures are very sensitive to changes in the cellular architecture, sPFG generally provides robust estimations only in highly organized white matter bundles. In less ordered tissue, it may provide little insight into the nature of that change, leading to common misinterpretations. For example, changes in FA are thought to represent white matter integrity, however, many factors (cell death, edema, gliosis, inflammation, change in myelination, increase in connectivity of crossing fibers, increase in extracellular or intracellular water, etc) may cause changes in FA. The limited specificity of measures such as FA and MD hinders our ability to relate the measurements to neuropathologies or to local anatomical changes such as differences in connectivity [24, 25, 26, 27]. In contrast to sPFG, non-conventional dMRI sequences can begin to bridge between the macro and micro levels of scale in the brain by providing information about distributions of cellular shapes, sizes and membrane properties within a voxel.
Building on the formal analogy between the chemical shift and diffusion anisotropy tensors, it has been shown that solid-state NMR (Nuclear Magnetic Resonance) techniques, such as “magic-angle spinning”, can be adapted to diffusion MRI [4]. In its simplest form, magic-angle spinning of the q-vector allows for estimation of the distribution of isotropic diffusivities free from the confounding influence of anisotropy.
WO 2013/165312 discloses how isotropic diffusion weighting of a diffusion weighted echo signal attenuation may be achieved by a continuous or discrete modulation of the dephasing vector q(t) such that an anisotropic contribution to the echo signal is minimized, for example by employing magic-angle spinning. WO 2013/165313 discloses a method for quantifying microscopic diffusion anisotropy and/or mean diffusivity by analysis of echo attenuation curves acquired with two different gradient modulation schemes, wherein one gradient modulation scheme is based on isotropic diffusion weighting and the other gradient modulation scheme is based on non-isotropic diffusion weighting. WO 2013/165313 discloses that non-isotropic diffusion weighting may be achieved for example using single-pulse gradient spin echo (PGSE).
Although these prior art methods enable separation of isotropic and anisotropic contributions to the echo signal attenuation and quantification of inter alia microscopic fractional anisotropy, it would in some cases be desirable to have a greater freedom in terms of the gradient modulation schemes used for causing the diffusion weighting and still be able to analyze and quantify microstructure properties such as microscopic diffusion anisotropy and/or mean diffusivity e.g. for the purpose of tissue characterization using diffusion spectroscopy. For example isotropic diffusion encoding may in some cases impose high requirements on the hardware with respect to slew rate and maximum magnitude which are difficult to meet with older and less expensive equipment.